Welcome to the forums! What are the hardware specs of your old, slow XP computer? (CPU, RAM, video card, network adapter, etc.) Have you given Mint a test-drive in "Live" mode yet? (to see if your hardware is supported and so forth)
Here is the documentation for Linux Mint 13: http://www.linuxmint.com/documentati...glish_13.0.pdf
The specific information about installing alongside XP can be found in the chapter titled "Install Linux Mint on your Hard Drive."
Good luck! Let us know if you have any specific questions, or if you encounter any errors/roadblocks along the way.